Exponential stability of impulsive conformable fractional-order nonlinear differential system with time-varying delay and its applications

Abstract

This paper investigates the exponential stability of conformable fractional-order nonlinear differential systems with time-varying delay and impulses. The authors utilize the principle of comparison and the Lyapunov function method to establish sufficient conditions that guarantee the exponential stability of a specific class of conformable fractional-order nonlinear differential systems. These findings extend the existing results on systems with integer-order to a certain extent. Furthermore, the paper considers the effect of impulses in the delayed system, which was not addressed in previous literature The authors also apply the criterion for exponential stability to conformable fractional-order neural networks. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed results.